How sensitive is the climate to added CO2?

65 million years of Earth's history suggest we're in uncharted territory.

As recent events have shown, even the World Bank is trying to understand the trajectory of future climate changes. Although there are a number of ways of doing this, many organizations rely on a measure called the climate sensitivity. It's a bit rough, but it's simple: it provides a value for the temperature increase we'd expect given a doubling of CO2.

Currently, the Intergovernmental Panel on Climate Change places this value between 2 and 4.5°C, with a most likely value of about 3°C. But a variety of studies have come up with measurements spread around that range, and nailing down the likely upper limit has been a challenge. Now, a large group of researchers has gone through millions of years of data on the Earth's past, incorporating information from a number of past studies. In the end, the group decided that the IPCC estimates are more or less on target.

Adding more carbon dioxide to the atmosphere doesn't drive temperatures in a linear manner. You can think of this in terms of the infrared photons they absorb: each one can only be absorbed once, and the more CO2 molecules you add, the more likely it is that an existing one would have absorbed that photon anyway. As a result, each doubling of carbon dioxide concentrations are expected to have roughly an equivalent impact.

What exactly is that impact? It's possible to calculate it from first principles. Put all the known forces and feedbacks into a climate model, double the CO2, and see what it produces after it reaches an equilibrium. That has been the method of choice for the IPCC, but the different climate models it uses produce a range of values, which is why its estimate runs from 2.1 to 4.4 K.

The alternative approach is to try to measure the climate sensitivity displayed by the planet during periods of major climate change in the past. Unfortunately, these estimates don't always agree with the IPCC's; even more unfortunately, they don't always agree with each other. Those disagreements are what prompted a large collaboration of researchers called the PALAEOSENS project to try to figure out what was going on.

Part of the problem with historic reconstructions is simply that we don't have all the data we'd like. Ice cores cover the last 800,000 years or so very well, and the gas bubbles trapped within provide a reasonable estimate of global atmospheric content. But they only capture the local temperatures well. And once you get beyond the ice cores, you have to rely on proxies for most of the data you want. Right now, we simply don't good proxies for some things, such as levels of methane, a potent greenhouse gas.

Another problem is that the Earth is a dynamic system. Some responses to rising temperatures are fairly rapid, such as the loss of snow cover (which has a cooling effect by reflecting sunlight back to space). Others are far more gradual. Oceans, for example, act as a giant heat sink that can slow down any warming for centuries. That makes nailing down the long-term equilibrium response very difficult. As the authors put it, "the timescales to reach this [climate] equilibrium are long, so... the forcing normally changes before equilibrium is reached."

Confusing matters even further, different papers have used subtly different methods of defining the climate sensitivity.

So, the team went back and reanalyzed a variety of existing studies using a single definition of climate sensitivity and separating rapid climate responses to changes in greenhouse gasses from the longer-term response needed for the climate to reach an equilibrium. The authors estimate that rapid responses account for about two-thirds of the total change in temperature and typically occur within 100 years.

With the reanalysis, a couple of things become clear. One is that the climate sensitivity varies over time. This was already known to a certain extent, in that the configuration of the continents can influence the climate independently of atmospheric and orbital influences. in this new analysis, the variability was also apparent in the ice cores, which cover only the last 800,000 years during which the continents were in roughly their current configuration. The changes are small—within about a half-Kelvin—but they indicate that the climate sensitivity is itself sensitive to the initial conditions on the planet.

Extending the analysis out to 65 million years, the authors calculate that there's about a 70 percent probability the IPCC has it right. More specifically, their 68 percent confidence range ran from 2.2 to 4.8 K; the 95 percent confidence interval was a bit broader, but it encompassed the IPCC's range.

More disturbingly, however, they calculate that we can go back to roughly when the dinosaurs died off and not see another period like the present: "Present-day atmospheric GHG [greenhouse gas] concentrations and the radiative perturbation due to anthropogenic emissions increase much faster than observed for any natural process within the Cenozoic era." We really do seem to be into uncharted territory here.

Thank you Daren, I am aware of the normal distribution and its application to the term "confidence interval". I am requesting that the 95% confidence interval be quoted, and asking if a 68 percent confidence interval (an interval I don't recall having encountered in scientific literature before) is standard in climate science.

Thank you Daren, I am aware of the normal distribution and its application to the term "confidence interval". I am requesting that the 95% confidence interval be quoted, and asking if a 68 percent confidence interval (an interval I don’t recall having encountered in scientific literature before) is standard in climate science.

The %68 is right in the title of the article linked. Climate science, being an actual science, of course uses standard statical mathematics as best practices.

Thank you Daren, I am aware of the normal distribution and its application to the term "confidence interval". I am requesting that the 95% confidence interval be quoted, and asking if a 68 percent confidence interval (an interval I don't recall having encountered in scientific literature before) is standard in climate science.

68% is one standard deviation, 95% is two and 99.7% is three (rule of thumb). He's reporting it like that because he's starting from the IPCC range and reporting the confidence in that range instead of going from a 95% confidence interval and reporting that range.

2. If we can always adapt to whatever is thrown at us, and get off this planet what does it matter?

I never understand this line of argument. By (Lord help me) analogy: Suppose that you, Scorp1us, through your own lack of prevention, get some preventable, disease. The disease is treatable, but at extraordinary cost - say all your limbs have to be cut off, you go blind, and live in pain for the rest of your life. You subsequently "adapt" to all this and live to be 100. Wouldn't you rather just not get the disease in the first place? There seems to be this idea that "adapting" to climate change will somehow be effortless and painless. I don't believe that's the case. And neither does the U.S. DoD..

All wonderful background that I was previously aware of. Does not answer my question.

joshv wrote:

What rhetorical point would that be?

Either you knew what a 68% confidence interval is and why it arises, or you didn't. If you did know, then you were asking a rhetorical question. How can I reconcile these statements while maintaining good faith?

Josh? How old is Josh? You should go work for NASA while you still know everything.

It is a sign of maturity to admit when one is wrong. It is a sign of adolescence to pretend one knows, and also to continue to insist you knew when everyone else already knows you didn't know. It just makes you look like an idiot. There's nothing wrong with a big ego. I got one too. But don't allow your ego defense to dig your hole deeper and deeper.

What' the big deal in admiting you learned something new today?

Anyhow. Great job Ars. We need more of these articles. Just the facts, ma'am.

All wonderful background that I was previously aware of. Does not answer my question.

joshv wrote:

What rhetorical point would that be?

Either you knew what a 68% confidence interval is and why it arises, or you didn't. If you did know, then you were asking a rhetorical question. How can I reconcile these statements while maintaining good faith?

Sorry, let me rephrase that portion of my question as it appears to have caused confusing. "Why is a 68% confidence interval used. Is it a standard in climate science?"

What's caused me confusing is that there is nothing special about quoting something at a 1 sigma level, yet you seem to think it is indicative of something sloppy/nefarious/conspiratorial in climate science that separates it from every other science.

Josh? How old is Josh? You should go work for NASA while you still know everything.

It is a sign of maturity to admit when one is wrong. It is a sign of adolescence to pretend one knows, and also to continue to insist you knew when everyone else already knows you didn't know. It just makes you look like an idiot. There's nothing wrong with a big ego. I got one too. But don't allow your ego defense to dig your hole deeper and deeper.

What' the big deal in admiting you learned something new today?

Anyhow. Great job Ars. We need more of these articles. Just the facts, ma'am.

I am 41 - and my questions have yet to be answered, though there seems to be a powerful urge to avoid them by misunderstanding them.

I want to know specifically what the 95% confidence range of values was from the quoted article - as in the min and max of the 95% confidence interval. I do not want to know what a confidence interval is, or what sigma a particular percentage corresponds to. If my question appeared to request that, I apologize for my lack of clarity.

I also want to know why a 68% confidence interval is quoted instead of the 95% confidence interval. I know that the linked article quotes that value. But I ask why is it used at all? Is it a standard in climate science? I've never previously encountered 68% confidence intervals in my readings of scientific literature. For example I've read extensively in medical literature and there the standard is a 95% interval, or better. In particle physics, I believe it's something like 5 or 6 sigma.

I am not sure what you are talking about when you say "It is a sign of adolescence to pretend one knows, and also to continue to insist you knew when everyone else already knows you didn't know. It just makes you look like an idiot." I am asking questions. If you have an answer, please provide it, and I will perhaps learn something. If you just want to call me an idiot - go away.

What's caused me confusing is that there is nothing special about quoting something at a 1 sigma level, yet you seem to think it is indicative of something sloppy/nefarious/conspiratorial in climate science that separates it from every other science.

Sloppy perhaps in the sense that it allows an extraordinarily large chance that the actual value falls outside of the quoted range. If climate scientists are ok with that, so be it. It's not a standard I've encountered in my readings in other branches of science. I have no idea as to the motives of the scientists involved. I doubt however that they are nefarious or conspiratorial.

Uncharted territory? I guess, if you ignore the periods in the past (more than 65m years ago) that had significantly higher CO2 concentrations than what we have now.

You mean when mammals were little critters living underground because they were hiding from DINOSAURS? That period? When the climate was drastically different? Supporting entirely different life forms than what we have today? Before humans existed? That period? Do you want to go back to that? What would happen to our cities and other infrastructure if we went back to that in a space of just a few decades?

That, my friend, is exactly why we are so alarmed at climate change.

It boggles the mind at the sort of apologist logic the deniers will come up with to justify non-action. We can't continue burning carbon! We are cutting the tree branch we are sitting on!

In case you are not familiar enough with statistics to understand the normal distribution wiki, a confidence interval is the likelihood that the true value lies within the stated range. It is not arbitrarily chosen. It is an "exact" mathematical range determined by a formula. The exact formula is available in the Wikipedia entry for confidence intervals.

I believe the 68% (1 sigma) value was quoted because that's where the range predicted by the IPCC lies. This study predicts a wider range at 95% confidence, though for whatever reason that range wasn't quoted.

What's caused me confusing is that there is nothing special about quoting something at a 1 sigma level, yet you seem to think it is indicative of something sloppy/nefarious/conspiratorial in climate science that separates it from every other science.

Sloppy perhaps in the sense that it allows an extraordinarily large chance that the actual value falls outside of the quoted range. If climate scientists are ok with that, so be it. It's not a standard I've encountered in my readings in other branches of science. I have no idea as to the motives of the scientists involved. I doubt however that they are nefarious or conspiratorial.

The 68% interval is quoted because that's most likely where the actual value is. If you don't like it, you can figure out approximately what the 95% interval is simply because it's twice as large as the 68% interval. Without even having to look at anything else. Nothing is really hidden there.

I wouldn't object to it being included in the article, but I don't see why its omission is a problem either.

Because they're saying "our model says there is a 68% chance that this other model is correct."

What is hard to understand about that?

That's the point they're trying to make.

I will note that about twice of the 95% confidence interval is above the IPCC's model - or, to put it simply, if the IPCC model is wrong, it is about twice as likely to be too low than too high - so it would be more likely to underestimate the true impact than overestimate it.

"Over the past 65 million years, this reveals a climate sensitivity (in K W−1 m2) of 0.3–1.9 or 0.6–1.3 at 95% or 68% probability, respectively. The latter implies a warming of 2.2–4.8 K per doubling of atmospheric CO2, which agrees with IPCC estimates."

Doing some rough math, that would suggest that the 95% confidence interval for temperature range is 1.1 - 7.0 K.

Josh, you should read some actual papers in science journals where you will see different confidence intervals used in a variety of ways. It's very common when predicting a range of numbers (such as a temperature range) to discuss several confidence intervals in the paper since that tells us different ranges at all of those confidence intervals.

You also need a quick refresher course on the difference between "odds" and "confidence intervals". Your statement about being close to a coin toss demonstrates your confusion on the subject.

You don't yet know enough about statistics in science to even ask intelligent questions yet. Don't get upset, just take some time and learn about how such statistics are used, then read a few dozen scientific papers to get a better feel for it.

Because they're saying "our model says there is a 68% chance that this other model is correct."

What is hard to understand about that?

Quote:

Nothing at all difficult to understand, but it's also saying that there is a 32% chance that the value lies outside of the range they quote. I just typically never encounter scientific results quoted to a one sigma range. If that's the standard in climate science so be it.

Titanium Dragon wrote:

"Over the past 65 million years, this reveals a climate sensitivity (in K W−1 m2) of 0.3–1.9 or 0.6–1.3 at 95% or 68% probability, respectively. The latter implies a warming of 2.2–4.8 K per doubling of atmospheric CO2, which agrees with IPCC estimates."

Doing some rough math, that would suggest that the 95% confidence interval for temperature range is 1.1 - 7.0 K.

Thank you - that's the interval I would expect to be quoted. That is a rather wide range of values don't you think?

What's caused me confusing is that there is nothing special about quoting something at a 1 sigma level, yet you seem to think it is indicative of something sloppy/nefarious/conspiratorial in climate science that separates it from every other science.

Sloppy perhaps in the sense that it allows an extraordinarily large chance that the actual value falls outside of the quoted range. If climate scientists are ok with that, so be it. It's not a standard I've encountered in my readings in other branches of science. I have no idea as to the motives of the scientists involved. I doubt however that they are nefarious or conspiratorial.

Here's the thing Josh. If you assume this is a normal distribution (which is reasonable) then knowing the +/- 1 sigma values COMPLETELY specifies the ENTIRE distribution. In the time it took you to write one post, you could have had the entire distribution function figured out.

EDIT: I See others posted back-of-the-envelope calculations while I showered.

joshv wrote:

Titanium Dragon wrote:

"Over the past 65 million years, this reveals a climate sensitivity (in K W−1 m2) of 0.3–1.9 or 0.6–1.3 at 95% or 68% probability, respectively. The latter implies a warming of 2.2–4.8 K per doubling of atmospheric CO2, which agrees with IPCC estimates."

Doing some rough math, that would suggest that the 95% confidence interval for temperature range is 1.1 - 7.0 K.

Thank you - that's the interval I would expect to be quoted. That is a rather wide range of values don't you think?

That's why a lot of climate science research is work being done to narrow those error bars down these days.

Josh, you should read some actual papers in science journals where you will see different confidence intervals used in a variety of ways. It's very common when predicting a range of numbers (such as a temperature range) to discuss several confidence intervals in the paper since that tells us different ranges at all of those confidence intervals..

I have read rather widely. I see many different intervals or p values used. Almost universally 95% (p=0.05) is the minimum standard. Though there are some that argue that event this is a rather lax standard.

kengi wrote:

You also need a quick refresher course on the difference between "odds" and "confidence intervals". Your statement about being close to a coin toss demonstrates your confusion on the subject.

There is a 32% chance that the actual value falls outside the range quoted in the article. That differs negligibly from 50/50 when compared to higher standards such as p<0.05 or p<0.01

kengi wrote:

You don't yet know enough about statistics in science to even ask intelligent questions yet. Don't get upset, just take some time and learn about how such statistics are used, then read a few dozen scientific papers to get a better feel for it.

I am not at all upset. My question goes right to the heart of the validity of this paper's results. If you'd like to school me, show me another branch of science where a 68% confidence interval is the norm.

I am not at all upset. My question goes right to the heart of the validity of this paper's results. If you'd like to school me, show me another branch of science where a 68% confidence interval is the norm.

This is really getting to the category of "so far off it's not even wrong" and conspiracy theories.

I am not at all upset. My question goes right to the heart of the validity of this paper's results. If you'd like to school me, show me another branch of science where a 68% confidence interval is the norm.

This is really getting to the category of "so far off it's not even wrong" and conspiracy theories.

What conspiracy are you talking about?

I am asking you to provide an example of a branch of science that regularly reports results with a 68% confidence interval. I have not encountered any, typically I see a much higher standard. If you would like to dispute that observation, please do. I am all ears, and I promise not to roll my eyes.

Thank you - that's the interval I would expect to be quoted. That is a rather wide range of values don't you think?

For a system as complex as the entire Earth, it's not unexpectedly wide.

I mean, there are feedback cycles here that we can only guess at right now, because the Earth is in uncharted territory. We can look at what happened in the past, we can try to understand the forcings and feedbacks from first principles, but we can't be certain because we don't have a second earth to compare with, and we don't have any historical parallels for the current situation, because it hasn't happened before.

There are feedbacks like permafrost melting that we are just beginning to work out. NASA will be presenting their research into this to the American Geophysical Union next week, and rumour has it that it will be well out of step with anything predicted by current models.

In fact, it's a testament to the skill, professionalism and effort of climate scientists that they have managed to develop coherent methods at all. All they can do is create the best models they can, and update them as new data comes to hand. That's what scientists do.

I am not at all upset. My question goes right to the heart of the validity of this paper's results. If you'd like to school me, show me another branch of science where a 68% confidence interval is the norm.

This is really getting to the category of "so far off it's not even wrong" and conspiracy theories.

What conspiracy are you talking about?

I am asking you to provide an example of a branch of science that regularly reports results with a 68% confidence interval. I have not encountered any, typically I see a much higher standard. If you would like to dispute that observation, please do. I am all ears, and I promise not to roll my eyes.

Perhaps the author was presenting the information in a way he thought was most useful. Rather than saying that there is a 95% chance that the sensitivity is between 1.1K and 7.0K, he said that there's a 68% chance that the sensitivity is between 2.2 K and 4.8K. The distribution behind this information is the same, and there is NO difference in 'validity' in these results.

Thank you - that's the interval I would expect to be quoted. That is a rather wide range of values don't you think?

Given the methodology used? Not really. I'd expect a pretty broad range. The fact that it agrees with other models is good, though - it means that the other models are more likely to be accurate, as they are in line with historical events, at least as close as historical events go.

If you look at various scenarios, most of the models peg climate change in the 1.1 - 7.0K range; this isn't the first model to suggest that 7K is very much a possibility, which is somewhat worrisome, and more recent models and indicators we have suggest that higher temperature change is more likely than lower ones. But the fact that a lot of independent sources are pointing towards similar scenarios in the 2-4 K range suggests that range is more likely to be correct.

Using a bunch of different datasets is actually a good way to increase confidence, as if they all agree to roughly the same range, or at least agree over a range, then that agreed upon range is more likely to be correct.

Quote:

There is a 32% chance that the actual value falls outside the range quoted in the article. That differs negligibly from 50/50 when compared to higher standards such as p<0.05 or p<0.01

Er, no?

32% is almost 50% different from 50%. That's a pretty big difference.

Quote:

I am not at all upset. My question goes right to the heart of the validity of this paper's results. If you'd like to school me, show me another branch of science where a 68% confidence interval is the norm.

Given that we've pointed out that the paper:

A) states its 95% confidence range.

AND

B) Talks about the 68% confidence range because it matches with ANOTHER MODEL'S confidence range (thereby making that model MORE LIKELY to be accurate, as you are having MULTIPLE MODELS match up)

I'm not sure what you're going on about.

In all fields of science people talk about their confidence intervals matching up with other confidence intervals. If you knew anything about science you would know this.

2. If we can always adapt to whatever is thrown at us, and get off this planet what does it matter?

I never understand this line of argument. By (Lord help me) analogy: Suppose that you, Scorp1us, through your own lack of prevention, get some preventable, disease. The disease is treatable, but at extraordinary cost - say all your limbs have to be cut off, you go blind, and live in pain for the rest of your life. You subsequently "adapt" to all this and live to be 100. Wouldn't you rather just not get the disease in the first place? There seems to be this idea that "adapting" to climate change will somehow be effortless and painless. I don't believe that's the case. And neither does the U.S. DoD..

Excellent analogy...but to play devil's advocate...what if (using your anology) the steps neccessary to prevent the disease included cutting off only two of your limbs? This is basically what is being asked of society...let us cut off two of your limbs so you may (or may not) contract a disease in the future that may (or may not) require removal of all your limbs...until the scientific community does a better job of selling the ability to predict the future, society is going to be be very wary of sacrificing a little something now over the chance they MAY have to sacrifice something in the future...human nature and all.

As for the article, I find the second to last paragraph to be the most interesting. That the location of the continents can influence the climate independently of atmospheric and orbital influences was not something I had really taken into account before. I wonder how many other things become clear after each reanalysis?

If I may take another shot at clearing up the 1-sigma vs. 2-sigma "debate":

95% confidence is typical for disproving the null hypothesis and establishing a correlation (e.g. showing that CO2 is a greenhouse gas, to use an example that's already well established). I'm pretty sure this is where joshv is getting the idea that it's the standard everything should be held to.

The paper discussed here isn't about establishing the statistical significance of anything. It's about providing a likely range for an important number. 1-sigma is completely appropriate for reporting that.